1. Field of the Invention
The present invention relates to a method for measuring distance in a digital type distance relay which is applied to an electric power system.
2. Description of the Prior Art
There has been known a system used in a digital type distance relay apparatus of which working principle is based on the following relational formula among voltage v, current i, resistance R, and inductance L of a power transmission line, ##EQU2## namely, simultaneous equations are set up with respect to R and L by providing the same with voltage and current values at two different time points, so that R and L are derived therefrom.
Concerning such a system, there are proposed one method to apply difference approximation to the differential term and another method to integrate both sides of the equation (1) to eliminate the differential term and thereafter to solve the then appearing integral term by approximation with the trapezoidal formula. While the equation (1) holds good regardless of the frequency of the voltage and current, since the differential or integral in the calculation is approximated with discrete values taken by sampling at constant time intervals as described above, it follows that the approximation formula has a frequency characteristic and as a result the thus calculated values of R and L also have a frequency characteristic. To improve such a frequency characteristic, the following methods have been proposed:
(I) "Protective Relay Apparatus", Japanese Patent Laid-open No. 60-39312 (1985); and
(II) "Algorithm for New Type Distance Relay", by Oura et al., Paper 1282 at National Conference of the Japan Society of Electric Engineering in 1985.
Both of these relate to numerical approximation of the differential term in the equation (1), and the method (II) is such that is included in the method stated in (I) and the most simplified and practical type of the same.
In the prior art methods, however, errors were produced in a wider frequency range. In the method (II), for example, representing the sampling time points at constant intervals by t.sub.n-2, t.sub.n-1, t.sub.n, t.sub.n+1, . . . and the sampled current values at the corresponding time points by i.sub.n-2, i.sub.n-1, i.sub.n, i.sub.n+1, . . . , the current differential value, i.sub.n-1/2 at the time point t.sub.n-1/2 in the middle of the time points t.sub.n and t.sub.n-1 is approximated by the following equation, EQU i.sub.n-1/2 .apprxeq.k.sub.1 (i.sub.n -i.sub.n-1)+k.sub.2 (i.sub.n+1 -i.sub.n-2)
As apparent from this equation, data of four samples at least were required for differential approximation at one time point in the prior art method mentioned in (I) or (II) above, and since at least one sampling period had to be shifted in order that the values R and L were obtained by solving the simultaneous equations of the form of (1) set up for different time points, after all data of five samples were required. Since, on the other hand, a protective relay is required to make a correct decision of a fault the earliest possible, it has been desired that the number of samples for the data used in the calculation is as small as possible.